1. Field of the Invention
The present invention relates to a hologram, comprising a hologram film in which a diffraction grating has been recorded, that can be used as a screen, an optical reflection element or the like, and to a hologram production process for continuous production of holograms which are copies of the same photographed object original.
2. Description of the Related Art
Hologram films made of photopolymers and gelatin dichromate are well known in the prior art as hologram optical elements (HOES) employing volume phase-type holograms.
When such hologram films are used for various hologram optical elements, increased nick resistance, moisture resistance and solvent resistance of the hologram films are often provided by joining the hologram film to a protective material such as a substrate made of glass or a polymer film via a bonding material, leaving the hologram film in a sealed state.
In cases where the hologram film is made of gelatin dichromate, it has been proposed to use epoxy-based adhesives with excellent moisture resistance as the bonding material. For hologram films made of photopolymers, bonding materials proposed for use have included an adhesive containing no plasticizer to prevent migration of the solvent from the polymer film, etc. (Japanese Unexamined Patent Publication (Kokai) No. 6-56484) and an adhesive comprising a polyfunctional acrylate and a polymerization initiator (Japanese Unexamined Patent Publication (Kokai) No. 3-157684).
The following are well-known examples of applications wherein various hologram optical elements are used as display apparatuses.
As a first example there may be mentioned a hologram screen wherein a hologram film bearing a recorded light diffuser is used as a screen.
As shown in the attached FIG. 2, the hologram film can be fabricated by irradiating a photopolymer, gelatin dichromate or the like with an object beam composed of scattered light created by passing light through a light diffuser, and a reference beam consisting of non-scattered light, and recording an interference pattern functioning as a diffraction grating, which is produced by the object beam and the scattered light on the photopolymer, gelatin dichromate, etc.
The hologram film is reinforced with a protective material or bonding material as described above to construct a hologram screen. In the hologram screen, irradiation of an irradiated beam containing image data onto the screen can display an image because of diffraction and scattering of the irradiated beam on the screen.
As a second example there may be mentioned a reflection-type hologram reflector element which employs a hologram film on which a recorded plane mirror, concave mirror, convex mirror, etc. has been recorded, and which functions as a mirror.
This hologram film can be fabricated by irradiating onto a photosensitive material an object beam obtained by reflection at a concave mirror or convex mirror and a reference beam consisting of non-reflected light.
This type of hologram film is reinforced by a protective material or bonding material as described above to construct a hologram screen or hologram reflector element.
In this hologram reflector element, reflection of an irradiated beam containing image data can display a virtual image behind the hologram reflector element. A lens function may also be provided to allow magnification or reduction of the virtual image depending on the type of concave mirror or convex mirror.
The holograms described above, however, are prone to heat shrinkage of the polymer films when the use environment is under a high temperature. In such cases, since the substrate of glass, etc. undergoes virtually no heat shrinkage, stress is created between the substrate of glass, etc. and the polymer film, and this stress causes a deformation of the hologram film that can alter the gradient of the interference pattern in the hologram film.
Interference patterns with various gradients are recorded in hologram films, and light irradiated onto the holograms is diffracted because these interference patterns function as diffraction gratings. The interference patterns become inclined in response to any deformation of the hologram films, and their directions are thus altered.
When light is irradiated onto a hologram film, the light is diffracted due to the interference pattern; however, even if it is diffracted by the same interference pattern before and after deformation of the hologram film, it is diffracted in a different direction after deformation than before deformation because the gradient of the interference pattern is altered. Consequently, as shown in the attached FIG. 7, a phenomenon occurs whereby the peak of the hologram spectral characteristics is shifted toward the long wavelength end or short wavelength end after heat shrinkage occurs.
A screen or reflector element made of the hologram described above utilizes a diffraction effect due to the interference pattern in the hologram film, and therefore when deformation of the hologram film occurs due to heat shrinkage of the polymer film, a problem occurs in that a hue difference is produced between the irradiated beam which is irradiated and the image obtained by diffraction or reflection, or the hue is different between the outer perimeter and inside of the hologram, making the image appear deformed.
Naturally, this problem does not occur if the protective material encapsulating the hologram film is composed entirely of the same material or of a substance with the same degree of heat shrinkage, but this is not practical either because of the following problems.
One of these problems is that when the hologram is a film, the hologram twists, altering the hue of the image and producing deformation of the image. It is therefore necessary to support the hologram film with a substrate. The production process becomes more complicated with a structure wherein the hologram film is sandwiched between substrates.
As a practical operating method, when the hologram screen is placed onto window glass or the like, the semi-completed product comprising the hologram film, polymer film and bonding material is affixed onto the window glass. It is not practically possible to affix the hologram film bonded to the substrate onto another window glass or the like without including air bubbles, etc. When air bubbles have been included, the air bubbles are seen over the image, making it difficult to view the image.
Moreover, when the hologram is used as a reflector element and a plane mirror has been recorded on the hologram film, a lens effect (concave mirror/convex mirror effect) is produced which magnifies or reduces the reflected virtual image of the hologram, or when a concave mirror or convex mirror has been recorded it has often been impossible to obtain the designed lens effect (see Embodiment 3 below).
These problems occur most notably around the perimeter of the hologram where stress readily accumulates (see Embodiments 2 and 3 below).
In light of these problems of the prior art, it is an object of the present invention to provide a hologram with excellent heat resistance.
The present invention also relates to a hologram production process for continuous production of holograms which are copies of the same photographed object original.
A conventional process for continuous production of the same hologram is known whereby a photographed object original is continuously copied onto a film-like, long photopolymer (Japanese Unexamined Patent Publication (Kokai) No. 9-90857).
As shown in FIG. 13 explained below, after the film-like photopolymer is fed to a supply roller and the photopolymer is affixed to the photographed object original, it is exposed to laser light to copy the photographed object original onto the photopolymer. This converts the photopolymer to a hologram.
The hologram is then released from the photographed object original and affixed onto a protective film to protect the soft, easily damaged hologram. It is then wound up on a winding roller and the hologram is stored in a wound state.
This allows continuous production of holograms which are copies of the same photographed object original. The holograms obtained by this process are also long, and are therefore used after appropriate cutting.
By the conventional process described above, however, there is a risk of uneven attachment of the protective film onto the hologram due to slight vibrations, etc. of the protective film, and this has resulted in possible string-like appearance defects in the hologram. Emboss-like appearance defects have also been a risk, because irregularities in the attachment roller are transferred to the soft hologram.
As a more detailed explanation, while an appropriate pressing force is applied when affixing the protective film to the hologram, the pressing force sometimes exceeds the appropriate pressing force because of variation due to vibrations when the protective film moves, irregularities in the roller, etc.
In such cases, deformations 351, 301 are produced in the protective film 215 and hologram 201, as shown in FIG. 16B explained below. Since the hologram 201 is soft the deformations 301 sometimes disappear by the elasticity of the hologram 201 itself, but in most cases deformations are almost never eliminated from the hologram 201 once it has been deformed, because the protective film 215 acts to secure the deformations in the hologram 201.
When a hologram screen is constructed with a hologram in which such deformation has occurred, and an image beam 320 is irradiated onto the hologram screen by a projector 232 as shown in FIG. 14 explained below, there has been a risk of string-like blemishes 291, emboss-like blemishes 292 and the like being reflected on the hologram screen 209 as shown in FIG. 15B, which can be clearly seen by the viewer 238. These blemishes 291, 292 overlap the image 310, and thus risk noticeably impairing the appearance of the image 310.
In light of these problems of the prior art, it is another object of the invention to provide a process for producing holograms which can prevent occurrence of appearance defects.
The first aspect of the invention is a hologram comprising a hologram film in which a diffraction grating has been recorded, a substrate situated on one side of the hologram film via a bonding material, and a polymer film situated on the other side of the hologram film via a bonding material, characterized in that the thickness of the polymer film is no greater than 100 xcexcm.
The most notable feature of this aspect is that the thickness of the polymer film is no greater than 100 xcexcm.
The polymer film undergoes heat shrinkage when the environment in which the hologram is used is under high temperature, but the substrate undergoes virtually no heat shrinkage. The hologram film is deformed by motion stress during heat shrinkage of the polymer film, but if the thickness of the polymer film is limited to no greater than 100 xcexcm as according to this aspect, it is possible to sufficiently reduce the stress acting on the hologram film.
It is thus possible to obtain a hologram in which deformation of the hologram film is minimized as is deformation of the interference pattern functioning as the diffraction grating recorded in the hologram film, which is a cause of deformation of the hologram film, while variation in the spectral characteristics and diffraction angle of the irradiated beam, for example, are also minimized (see Embodiments 2 and 3 below).
According to this aspect, holograms with excellent heat resistance can be provided.
If the thickness of the polymer film exceeds 100 xcexcm there will be greater contraction force due to heat shrinkage of the polymer film, thus risking deformation of the hologram film and alteration of the hue and shape of the image. The contraction force is directly proportional to the thickness of the polymer film.
The lower limit for the thickness of the polymer film is preferably 25 xcexcm, in order to guarantee damage resistance and ease of fabrication during production.
The polymer film used may be polyethylene terephthalate (PET), polycarbonate (PC), triacetyl cellulose (TAC) or the like. The substrate used may be a glass substrate, acrylic substrate, polycarbonate substrate or the like.
The surface side of the polymer film (the side exposed to the outside) may be supplied with a hard coat film for improved damage resistance or with an anti-reflection film or anti-glare film to reduce surface reflection.
A coloring agent may be combined with the polymer film itself for coloration of the hologram itself, or a colored polymer film designed to attract attention may be used. The effect of the coloring to attract attention is particularly effective in the case of a hologram screen.
The bonding material used may be a tackifier, hot-melt agent, adhesive or the like.
The polymer film used can also be an adhesive film wherein the polymer film and bonding material are integrated.
The second aspect of the invention is a hologram comprising a hologram film in which a diffraction grating has been recorded, a first polymer film situated on one side of the hologram film via a bonding material, a substrate situated via a bonding material on the side of the first polymer film on which the hologram film is not situated, and a second polymer film situated on the other side of the hologram film via a bonding material, characterized in that the thickness of the first polymer film is no greater than 150 xcexcm.
By limiting the thickness of the first polymer film to no greater than 150 xcexcm it is possible to sufficiently reduce stress acting on the hologram film and thus minimize deformation of the hologram film, similar to the first aspect.
It is thereby possible to obtain a hologram in which deformation of the interference pattern functioning as the diffraction grating, which causes deformation of the hologram film, is minimized, and changes in the spectral characteristics, etc. by heat are minimized.
According to the second aspect there may be provided holograms with excellent heat resistance.
If the thickness of the first polymer film exceeds 150 xcexcm the contraction force due to heat shrinkage of the polymer film will be greater, thus risking deformation of the hologram film and alteration of the hue and shape of the image.
The lower limit for the thickness of the polymer film is preferably 25 xcexcm from the standpoint of easier fabrication during production, but the first polymer film may be absent since this will not affect the damage resistance.
The other details are the same as explained above for the first aspect.
The third aspect of the invention is a hologram comprising a hologram film in which a diffraction grating has been recorded, a substrate situated on one side of the hologram film via a bonding material, and a polymer film situated on the other side of the hologram film via a bonding material, characterized in that the polymer film has been subjected to prior heat treatment.
Heat shrinkage of the polymer film is an irreversible change. Addition of the prior heat treatment can therefore produce sufficient heat shrinkage of the polymer film.
This can prevent heat shrinkage of the polymer film after the hologram has been formed, thus minimizing deformation of the hologram film.
It is thereby possible to obtain a hologram in which deformation of the interference pattern functioning as the diffraction grating, which causes deformation of the hologram film, is minimized, and changes in the spectral characteristics, etc. by heat are minimized.
According to the third aspect it is possible to provide holograms with excellent heat resistance.
The optimum temperature and optimum heat time for the heat treatment will differ depending on the quality, thickness, etc. of the polymer film, but for example when the polymer film consists of a polyester film with a thickness of 100-200 xcexcm, a temperature of 80-150xc2x0 C. and a heating time of 30 minutes to 6 hours is preferred.
By satisfying these heating conditions it is possible to obtain a polymer film that has sufficient heat shrinkage and is resistant to any further shrinkage.
The fourth aspect of the invention is a hologram comprising a hologram film in which a diffraction grating has been recorded, a first polymer film is situated on one side of the hologram film via a bonding material, a substrate is situated via a bonding material on the side of the first polymer film on which the hologram film is not situated, and a second polymer film is situated on the other side of the hologram film via a bonding material, characterized in that the first polymer film has been subjected to prior heat treatment.
This heat treatment can prevent heat shrinkage of the first polymer film after the hologram has been formed, thus minimizing deformation of the hologram film.
It is thereby possible to obtain a hologram in which deformation of the interference pattern functioning as the diffraction grating, which causes deformation of the hologram film, is minimized, and changes in the spectral characteristics, etc. by heat are minimized.
According to the fourth aspect it is possible to provide holograms with excellent heat resistance.
The other details are the same as explained above for the third aspect.
According to the first to fourth aspects, the polymer film preferably has a polarizing optical property.
The hologram displays an image by diffraction/scattering or reflection of an incident image beam, but diffraction/scattering and reflection of light other than the image beam also occurs. This noise light in addition to the image beam often impairs the visibility of the image.
Since light other than the image beam is usually light of random polarization, by converting the image beam to a linear polarized beam aligned with the transmission axis of the polarizing polymer film it is possible to obtain an effect whereby the noise light is removed from the image since the noise light which is light of random polarization is absorbed by the polarizing polymer film, while the polarizing polymer film has absolutely no effect on the image beam which is a linear polarized beam.
The polarizing optical property is an optical property whereby the transmission differs depending on the direction of light polarization. Specifically, the transmission of light of random polarization wherein the direction of polarization is scattered is about 50%, and virtually all of the linear polarized light with the same direction of polarization is transmitted. However, virtually all linear polarized light having a direction of polarization shifted by 90xc2x0 is absorbed, so that the transmission is about 0%.
The hologram is preferably a hologram screen displaying an image by diffraction or scattering of an irradiated beam containing image data.
Upon irradiation of the irradiated beam which has recorded image data on the hologram, the irradiated beam is diffracted by the interference pattern of the hologram film, becoming diffracted light.
The holograms according to the aforementioned first to fourth aspects of the invention have minimal deformation of the hologram films and minimal deformation of the interference patterns in the hologram films. Alterations in the direction of diffraction due to deformation of the interference patterns are therefore prevented, so that changes in the spectral characteristics of the holograms can thus be minimized.
It is therefore possible to obtain hologram screens which produce minimal hue between the irradiated beam and the image displayed on the screen, even when used at high temperatures.
The hologram is preferred to be a hologram reflector element that displays a virtual image by reflecting image data irradiated as an irradiated beam.
According to the prior art, heat shrinkage of the polymer film has partially altered the curvature of concave or convex surfaces in cases where the diffraction grating recorded on the hologram film has a concave shape or convex shape. A problem has therefore existed in that the magnification rate of the displayed image changes, thus warping the image.
The hologram of the present invention, however, has high heat resistance which prevents heat shrinkage of the polymer film, and therefore it is possible to obtain a hologram reflector element with minimal image warping even when used at high temperatures.
The fifth aspect of the invention is a hologram production process which is a continuous production process for holograms whereby there is prepared a photopolymer coated onto a substrate and the photopolymer surface of the photopolymer is affixed onto a photographed object original, after which it is exposed to laser light to copy the photographed object original onto the photopolymer to convert it into a hologram, the hologram is then released from the photographed object original together with the substrate to expose the hologram surface of the hologram, and finally a protective film is affixed onto the hologram surface, characterized in that the bonding strength A between the substrate and the hologram is greater than the bonding strength B between the hologram and the protective film.
If the bonding strength A is less than the bonding strength B, there is a risk that when the hologram undergoes deformation due to uneven external forces, etc. when the protective film is affixed onto the hologram, the deformation of the hologram will be transferred completely to the protective film (see FIG. 16B described below). The possibility exists that the deformed protective film may keep the deformed state of the hologram even after the external force has ceased.
According to this aspect, the protective film used may be one comprised of, for example, polyethylene, polyester, polypropylene, etc.
The substrate may also be one comprised of, for example, polyethylene, polyester, polypropylene, etc., similar to the protective film.
The photopolymer used may be, for example, a photopolymerizing or photocrosslinking type of material.
The protective film is provided to protect the hologram surface of the hologram, and it may be removed for actual use of the hologram.
The substrate and hologram are bonded together by the viscosity of the photopolymer itself.
The hologram and the protective film may be bonded, for example, by introducing the hologram and the protective film between two attachment rollers to affix them together, as shown in FIG. 12D described below.
The bonding strength between the substrate and the hologram is preferably 150-800 g/50 mm. If it is less than this range the hologram (photopolymer) may be damaged when the hologram is released from the photographed object original. If it is greater than this range, it may become very difficult to remove the substrate after formation of the hologram.
The photographed object original may be copied by affixing the photopolymer onto the photographed object original and then irradiating it with laser light to expose the photopolymer to laser light. The laser light irradiation can be accomplished from the side of the substrate 211 and the photopolymer 210 as in FIG. 12B, or from the side of the photographed object original as in FIG. 13. A reflecting-type hologram can be fabricated in the former case, and a transmission-type hologram in the latter case.
The photopolymer surface is the surface on the side opposite the side on which the substrate is bonded. The hologram surface is on the same side as the photopolymer surface, and it is the surface which had been affixed to the photographed object original (see FIG. 1).
The most notable feature of the fifth aspect is that the bonding strength A between the substrate and hologram is greater than the bonding strength B between the hologram and protective film.
When the protective film 215 is affixed to the hologram 201 with the substrate 211 attached as shown in FIG. 16A, deformed sections 301, 351 are formed on the protective film 215 and the hologram 201, as shown in FIG. 16B.
Since the hologram 201 obtained by the production process according to the fifth aspect has higher bonding strength between the substrate 211 and the hologram 201, the hologram 201 becomes anchored to the substrate 211. In comparison to the substrate 211, the protective film 215 is in a freer state with respect to the hologram 201.
Thus, as shown in FIG. 16B, the deformed sections 301 of the hologram 201 are removed by the restoring force F of the hologram 201, and the deformed sections 351 of the protective film 215 are removed by the restoring force of the protective film 215, resulting in a hologram 201 and protective film 215 with virtually no deformed sections 301, 351, as shown in FIG. 16C.
According to this fifth aspect, it is possible to provide a process for the production of holograms with minimal appearance defects.
When the hologram is used as a screen and an image beam is irradiated from a projector onto the hologram screen as shown for example in FIG. 14 described below, the appearance defects that are caused by the deformed sections of the hologram can be clearly seen by viewers as string-like blemishes or emboss-like blemishes over the image, as shown in FIG. 15B described below.
When the hologram is used as a screen, a plurality of diffraction gratings are recorded on the hologram, but when the hologram contains deformed sections, the diffraction gratings lose their shape as a result of the deformed sections, thus presenting appearance defects.
The protective film affixed to the hologram surface is preferably a release film provided with at least one type of coating selected from among silicon-based, olefin-based and fluorine-based coatings on at least the attachment surface. The use of such a release film allows the effect of the fifth aspect to be adequately achieved.
After the hologram has been released from the photographed object original, the hologram is subjected to polymerization treatment until attachment of the protective film, and the bonding strength A between the substrate and the hologram is preferably greater than the bonding strength B between the hologram and the protective film.
The hologram will have a higher hardness if the polymerization ratio is higher. A higher hardness minimizes deformation, etc., and therefore this polymerization treatment can give a hologram with fewer appearance defects. A higher polymerization ratio also results in lower viscosity, and is preferred in order to lower the bonding strength between the hologram and the protective film.
The polymerization ratio of the hologram is preferably 50-100%. This makes it possible to consistently achieve an effect of increased hardness by the polymerization ratio.
If the polymerization ratio is under 50% there is a risk of insufficient hardness which may result in deformation of the hologram during attachment, producing appearance defects.
The polymerization treatment is preferably carried out by heating and/or ultraviolet irradiation of the hologram.
This allows the polymerization treatment to be accomplished easily due to reaction of the unreacted monomers. The hologram can therefore be easily hardened.
xe2x80x9cHeating and/or ultraviolet irradiationxe2x80x9d refers to heating and ultraviolet irradiation, or heating alone or ultraviolet irradiation alone.
When both heating and ultraviolet irradiation are carried out, they may be carried out simultaneously or separately. The heating temperature, heating time, and the ultraviolet wavelength, intensity and irradiation time will differ depending on the type of photopolymer, the thickness of the photopolymer, etc.
The sixth aspect of the invention is a hologram production process which is a continuous production process for holograms whereby there is prepared a photopolymer coated onto a substrate and the photopolymer surface of the photopolymer is affixed onto a photographed object original, after which it is exposed to laser light to copy the photographed object original onto the photopolymer to convert it into a hologram, the hologram is then released from the photographed object original together with the substrate to expose the hologram surface of the hologram, and finally a protective film is affixed onto the hologram surface, characterized in that at least the attachment surface of the protective film is coated with at least one type of tackifier 159 as shown in FIG. 18, selected from among synthetic resin-based, synthetic rubber-based, silicone-based and polyurethane-based tackifiers.
If no tackifier is present, the hologram will sometimes undergo deformation by external force during attachment of the protective film onto the hologram, and this hologram deformation will be completely retained by the protective film. The deformation of the hologram can thus completely remain even after the external force has ceased.
By providing a tackifier as a buffer layer between the hologram and the protective film, it is possible to obtain a hologram with few appearance defects because deformation of the hologram by external force is prevented.
The thickness of the tackifier is preferably 1 xcexcm to 3 mm. If it is lower than this range it cannot perform its role as a buffer layer, and the buffer layer may provide an inadequate effect. If it is higher than this range the tackifier may bleed from the protective film when the protective film with the tackifier passes through the mounting section 225 of the light exposure apparatus 202, as shown in FIG. 13, thus creating an inconvenience.
The hardness of the tackifier is preferably softer than the hologram. This will provide a further buffering effect.
The seventh aspect of the invention is a hologram production process which is a continuous production process for holograms whereby there is prepared a photopolymer coated onto a substrate and the photopolymer surface of the photopolymer is affixed onto a photographed object original, after which it is exposed to laser light to copy the photographed object original onto the photopolymer to convert it into a hologram, the hologram is then released from the photographed object original together with the substrate to expose the hologram surface of the hologram, and finally a protective film is affixed onto the hologram surface, characterized in that the bonding strength between the hologram and the protective film is no greater than 200 g/50 mm.
The bonding strength is determined by the degree of force applied when a 50-mm wide affixed protective film and the hologram are peeled apart at 180xc2x0 at a rate of 300 mm/min.
If the bonding strength is greater than 200 g/50 mm, the hologram will be strongly anchored on both the protective film-hologram side and the substrate-hologram side, and this may make it difficult to restore deformation by the elasticity of the hologram.
According to the seventh aspect it is possible to obtain a hologram wherein the bonding strength between the hologram and the protective film is within the range specified above.
Since the bonding strength between the hologram 201 and the protective film 215 is sufficiently low, the deformed sections 301, 351 of the hologram 201 and the protective film 215 are removed by the restoring force F of the hologram 201 itself, as shown in FIG. 16B explained below, resulting in a hologram 201 and protective film 215 with virtually no deformed sections 301, 351, as shown in FIG. 16C.
Thus, according to the seventh aspect it is possible to obtain a hologram wherein deformation of the hologram by external force is prevented, thus reducing appearance defects.
The protective film affixed onto the hologram surface is preferably a release film provided with at least one type of coating selected from among silicon-based, olefin-based and fluorine-based coatings on at least the attachment surface. The use of such a release film allows the effect of the seventh aspect to be adequately achieved.
After the hologram has been released from the photographed object original, the hologram is subjected to polymerization treatment until attachment of the protective film, and the bonding strength A between the hologram and the protective film is preferably no greater than 200 g/50 mm.
The hologram will have a higher hardness if the polymerization ratio is higher. A higher hardness minimizes deformation, etc., and therefore this polymerization treatment can give a hologram with fewer appearance defects.
The polymerization treatment is preferably carried out by heating and/or ultraviolet irradiation of the hologram.
This allows the polymerization treatment to be accomplished easily due to reaction of the unreacted monomers. The hologram can therefore be easily hardened.
The details have already been explained above.
The bonding strength is more preferably 5-150 g/50 mm.
This will allow the effect of the seventh aspect to be achieved more consistently.
If the bonding strength is less than 5 g/50 mm, air bubbles will tend to be included between the hologram and the protective film when they are affixed together, and traces of the air bubbles will remain in the hologram and may cause appearance defects.
If the bonding strength is greater than 150 g/50 mm, there will be a possibility of larger emboss-like blemishes (see Embodiment 4).
According to aspects 5 to 7, a diffuser panel with a screen effect is preferably recorded in the hologram.
This makes it possible to obtain a hologram able to constitute an excellent screen with minimal blemishes, etc. in reflected images (see FIG. 15A).